Question F12.9: The boards are bolted together to form the built-up beam. If......
The boards are bolted together to form the built-up beam. If the beam is subjected to a shear force of V = 15 kip, determine the maximwu spacings of the bolts lo the nearest \tfrac{1}{8} in. if each bolt has a shear strength of 6 kip.
Consider center board and four side boards.
\begin{aligned} I & =\frac{1}{12}(1)\left(6^{3}\right)+4\left[\frac{1}{12}(0.5)\left(4^{3}\right)+0.5(4)\left(3^{2}\right)\right] \\ & =100.67 \mathrm{in}^{4} \end{aligned}
Top-right board is held onto beam by a row of bolts.
Q=y^{\prime} A^{\prime}=3(4)(0.5)=6 \text { in }^{3}Bolts have one shear surface.
q_{\text {allow }}=\frac{F}{s}=\frac{6}{s}
q_{\text {allow }}=\frac{V Q}{I} ; \quad \frac{6}{s}=\frac{15(6)}{100.67}
s=6.711 \text { in. }
Use s=6 \frac{5}{8} in.
Also, can consider the top two boards held onto beam by a row of bolts with two shearing surfaces.